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PF? That's how I do it and still make them all different. ;-)

Good question. If you want to keep the domain, ##D##, simply connected, you can not include any point on the negative reals (the branch...

That is sort of what I do. I keep all mine in PasswordSafe. Most that I very rarely use can be any random thing and I can look them up...

Mnemonics. "Mum very easily made a jam sandwich using no peanutbutter." = Merkur, Venus, Earth, Mars, The Asteroid Belt, Jupiter...

Yes. Expanding ##(z - a)^{-k}## in binomial series can be done in two ways; one converges for ##|z| < |a|## and the other for ##|z| > |a|##.

Series (2) can not converge at ##z=\sqrt 2## because the function is not defined there. The region of convergence (##1 \lt |z| \lt...

Yes. No. No. The flashes are simultaneous in at most one frame. That frame will report them as being simultaneous, others will not.

All of our experiments done to date over more than a century indicate that reality is accurately described by special relativity on a...

I don't believe there is a Laurent series for that function that converges for ##1 \lt |z| \lt \infty##

There are nice memory tricks for passwords that are good -- until you have a dozen to remember and you are occasionally forced to change...

Are you sure this problem is valid? The domains of the two expansions would make more sense to me if the function was ##\frac...

True, up to a point but Apple are never above pulling the wool over the consumers' eyes. Virtually no one ever does numerical analysis...

That could be a fruitful thread on its own but we all know there is no limit, only disposable income.

It depends on the applications. For a PC, gamers have driven the demands for increased CPU and graphics capability for a long time...

Absolutely! My iPhone has passwords, contact information, messages, map locations, etc. It would be a real problem if they were all gone...